New Synthetic Control Charts for Monitoring Process Mean and Process Dispersion

A statistical quality control chart is widely recognized as a potentially powerful tool that is frequently used in many manufacturing and service industries to monitor the quality of the product or manufacturing processes. In this paper, we propose new synthetic control charts for monitoring the process mean and the process dispersion. The proposed synthetic charts are based on ranked set sampling (RSS), median RSS (MRSS), and ordered RSS (ORSS) schemes, named synthetic‐RSS, synthetic‐MRSS, and synthetic‐ORSS charts, respectively. Average run lengths are used to evaluate the performances of the control charts. It is found that the synthetic‐RSS and synthetic‐MRSS mean charts perform uniformly better than the Shewhart mean chart based on simple random sampling (Shewhart‐SRS), synthetic‐SRS, double sampling‐SRS, Shewhart‐RSS, and Shewhart‐MRSS mean charts. The proposed synthetic charts generally outperform the exponentially weighted moving average (EWMA) chart based on SRS in the detection of large mean shifts. We also compare the performance of the synthetic‐ORSS dispersion chart with the existing powerful dispersion charts. It turns out that the synthetic‐ORSS chart also performs uniformly better than the Shewhart‐R, Shewhart‐S, synthetic‐R, synthetic‐S, synthetic‐D, cumulative sum (CUSUM) ln S², CUSUM‐R, CUSUM‐S, EWMA‐ln S², and change point CUSUM charts for detecting increases in the process dispersion. A similar trend is observed when the proposed synthetic charts are constructed under imperfect RSS schemes. Illustrative examples are used to demonstrate the implementation of the proposed synthetic charts. Copyright © 2014 John Wiley & Sons, Ltd.     

A New Synthetic Exponentially Weighted Moving Average Control Chart for Monitoring Process Dispersion

Exponentially weighted moving average (EWMA) control charts have been widely recognized as a potentially powerful process monitoring tool of the statistical process control because of their excellent speed in detecting small to moderate shifts in the process parameters. Recently, new EWMA and synthetic control charts have been proposed based on the best linear unbiased estimator of the scale parameter using ordered ranked set sampling (ORSS) scheme, named EWMA‐ORSS and synthetic‐ORSS charts, respectively. In this paper, we extend the work and propose a new synthetic EWMA (SynEWMA) control chart for monitoring the process dispersion using ORSS, named SynEWMA‐ORSS chart. The SynEWMA‐ORSS chart is an integration of the EWMA‐ORSS chart and the conforming run length chart. Extensive Monte Carlo simulations are used to estimate the run length performances of the proposed control chart. A comprehensive comparison of the run length performances of the proposed and the existing powerful control charts reveals that the SynEWMA‐ORSS chart outperforms the synthetic‐R, synthetic‐S, synthetic‐D, synthetic‐ORSS, CUSUM‐R, CUSUM‐S, CUSUM‐ln S², EWMA‐ln S² and EWMA‐ORSS charts when detecting small shifts in the process dispersion. A similar trend is observed when the proposed control chart is constructed under imperfect rankings. An application to a real data is also provided to demonstrate the implementation and application of the proposed control chart. Copyright © 2014 John Wiley & Sons, Ltd.     

A new adaptive EWMA control chart for monitoring the process dispersion

The exponentially weighted moving average (EWMA), cumulative sum (CUSUM), and adaptive EWMA (AEWMA) control charts have had wide popularity because of their excellent speed in tracking infrequent process shifts, which are expected to lie within certain ranges. In this paper, we propose a new AEWMA dispersion chart that may achieve better performance over a range of dispersion shifts. The idea is to first consider an unbiased estimator of the dispersion shift using the EWMA statistic, and then based on the magnitude of this shift, select an appropriate value of the smoothing parameter to design an EWMA chart, named the AEWMA chart. The run length characteristics of the AEWMA chart are computed with the help of extensive Monte Carlo simulations. The AEWMA chart is compared with some of the existing powerful competitor control charts. It turns out that the AEWMA chart performs substantially and uniformly better than the EWMA‐S², CUSUM‐S², existing AEWMA, and HHW‐EWMA charts when detecting different kinds of shifts in the process dispersion. Moreover, an example is also used to explain the working and implementation of the proposed AEWMA chart.     

Memory‐Type Control Charts for Monitoring the Process Dispersion

Control charts have been broadly used for monitoring the process mean and dispersion. Cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts are memory control charts as they utilize the past information in setting up the control structure. This makes CUSUM and EWMA‐type charts good at detecting small disturbances in the process. This article proposes two new memory control charts for monitoring process dispersion, named as floating T ? S² and floating U ? S² control charts, respectively. The average run length (ARL) performance of the proposed charts is evaluated through a simulation study and is also compared with the CUSUM and EWMA charts for process dispersion. It is found that the proposed charts are better in detecting both positive as well as negative shifts. An additional comparison shows that the floating U ? S² chart has slightly smaller ARLs for larger shifts, while for smaller shifts, the floating T ? S² chart has better performance. An example is also provided which shows the application of the proposed charts on simulated datasets. Copyright © 2013 John Wiley & Sons, Ltd.     

The Design of the ARL‐Unbiased S2 Chart When the In‐Control Variance Is Estimated

The S² chart has been known as a powerful tool to monitor the variability of the normal process. When the variance of the process is unknown, it needs to be estimated by Phase I samples. It is well known that there are serious effects of parameter estimation on the performance of the S² chart based on known parameter assumption. If the effects of parameter estimation are not considered, it can lead to an increase in the number of false alarms and a reduction in the ability of the chart to detect process changes except for very small shifts in the variance. Based on the criterion of average run length (ARL) unbiased, a S² control chart is developed when the in‐control variance is estimated. The performance of the proposed control chart is also evaluated in terms of the ARL and standard deviation of the run length. Finally, an example is used to illustrate the proposed control chart. Copyright © 2013 John Wiley & Sons, Ltd.     

A New Combined Shewhart–Cumulative Sum S Chart for Monitoring Process Standard Deviation

The combined application of a Shewhart chart and cumulative sum (CUSUM) control chart is an effective tool for the detection of all sizes of process shifts as the scheme combines the advantages of a CUSUM at detecting small to moderate shifts and Shewhart for the quick detection of very large shifts. This article proposes new combined Shewhart–CUSUM S charts based on the extreme variations of ranked set sampling technique, for efficient monitoring of changes in the process dispersion. Using Monte Carlo simulations, the combined scheme is designed to minimize the average extra quadratic loss over the entire process shift domain. The results show that the combined Shewhart–CUSUM S charts uniformly outperform several other procedures for detecting increases and decreases in the process variability. Moreover, the proposed scheme can detect changes that are small enough to escape the Shewhart S chart or fairly large to escape detection by the CUSUM S chart. Numerical example is given to illustrate the practical application of the proposed scheme using real industrial data. Copyright © 2015 John Wiley & Sons, Ltd.     

An enhanced CUSUM‐t chart for process mean

In this paper, we propose an auxiliary‐information–based (AIB) Crosier cumulative sum (CCUSUM) t chart for monitoring the process mean, namely, the AIB‐CCUSUM‐t chart. The run length characteristics of the proposed chart are computed using Monte Carlo simulation. The optimal parameters for the AIB‐CCUSUM‐t chart to detect specific mean shifts are computed. The fast initial response (FIR) feature is also attached with the proposed chart. It is found that the AIB‐CCUSUM‐t and FIR‐AIB‐CCUSUM‐t charts perform uniformly and substantially better than the CCUSUM‐t and FIR‐CCUSUM‐t charts, respectively. An example is presented to support the theory.     

Multivariate charting techniques: a review and a line‐column approach

The primary objective of multivariate statistical process control is to monitor the related process quality characteristics over time and identify the assignable causes affecting the process using multivariate control charts. When an out‐of‐control signal is obtained from the chart, it is imperative to be able to detect the component variables that have gone out‐of‐control. In this paper we propose a new charting procedure for T², multivariate exponentially weighted moving average and multivariate cumulative sum control charts. The proposed charts will facilitate in identification of the source of out‐of‐control signal and are simple, economical and easier to implement. Copyright © 2009 John Wiley & Sons, Ltd.     

The Run Sum Hotelling's χ2 Control Chart with Variable Sampling Intervals

Control charts are widely used for process monitoring and quality control in manufacturing industries. Implementing variable sampling interval (VSI) control schemes on control charts rather than traditional fixed sampling interval procedure can significantly improve the control chart's efficiency. In this paper, the VSI run sum (RS) Hotelling's χ² chart is proposed. The optimal scores and parameters of the proposed chart are determined using an optimization technique to minimize the following: (i) out‐of‐control average time to signal (ATS); (ii) adjusted ATS (AATS), when the exact shift size can be specified; (iii) expected ATS; or (iv) expected AATS, when the exact shift size cannot be specified. The Markov chain method is used to evaluate the zero‐state ATS and expected ATS, and steady‐state AATS and expected AATS of the proposed chart. The results show that the VSI RS Hotelling's χ² chart significantly outperforms the standard RS Hotelling's χ² chart and the former also performs well compared with other competing charts. By adding more scoring regions, the efficiency of the VSI RS Hotelling's χ² chart can be further enhanced. An illustrative example using data from a manufacturing process is presented to demonstrate the application of the VSI RS Hotelling's χ² chart. The application of the proposed chart in a quality improvement program can be extended to management and service industries. Copyright © 2016 John Wiley & Sons, Ltd.     

Alternative Hotelling's T2 Charts using Winsorized Modified One‐Step M‐estimator

Hotelling's T² chart is a popular tool for monitoring statistical process control. However, this chart is sensitive in the presence of outliers. To alleviate the problem, this paper proposed alternative Hotelling's T² charts for individual observations using robust location and scale matrix instead of the usual mean vector and the covariance matrix, respectively. The usual mean vector in the Hotelling T² chart is replaced by the winsorized modified one‐step M‐estimator (MOM) whereas the usual covariance matrix is replaced by the winsorized covariance matrix. MOM empirically trims the data based on the shape of the data distribution. This study also investigated on the different trimming criteria used in MOM. Two robust scale estimators with highest breakdown point, namely S_n and T_n were selected to suit the criteria. The upper control limits for the proposed robust charts were calculated based on simulated data. The performance of each control chart is based on the false alarm and the probability of outlier's detection. In general, the performance of an alternative robust Hotelling's T² charts is better than the performance of the traditional Hotelling's T² chart. Copyright © 2012 John Wiley & Sons, Ltd.     

Optimal designs of the multivariate synthetic chart for monitoring the process mean vector based on median run length

The average run length (ARL) is usually used as a sole measure of performance of a multivariate control chart. The Hotelling's T², multivariate exponentially weighted moving average (MEWMA) and multivariate cumulative sum (MCUSUM) charts are commonly optimally designed based on the ARL. Similar to the case of univariate quality control, in multivariate quality control, the shape of the run length distribution changes in accordance to the magnitude of the shift in the mean vector, from highly skewed when the process is in‐control to nearly symmetric for large shifts. Because the shape of the run length distribution changes with the magnitude of the shift in the mean vector, the median run length (MRL) provides additional and more meaningful information about the in‐control and out‐of‐control performances of multivariate charts, not given by the ARL. This paper provides a procedure for optimal designs of the multivariate synthetic T² chart for the process mean, based on MRL, for both the zero and steady‐state modes. Two Mathematica programs, each for the zero state and steady‐state modes are given for a quick computation of the optimal parameters of the synthetic T² chart, designed based on MRL. These optimal parameters are provided in the paper, for the bivariate case with sample sizes, nin{4, 7, 10}. The MRL performances of the synthetic T², MEWMA and Hotelling's T² charts are also compared. Copyright © 2011 John Wiley & Sons, Ltd.     

A CCC‐r chart for high‐yield processes

The cumulative count of a conforming (CCC) chart is used to monitor high‐quality processes and is based on the number of items inspected until observing r non‐conforming ones. This charting technique is known as a CCC‐r chart. The function of the CCC‐r chart is the sensitive detection of an upward shift in the fraction defectives of the process, p. As r gets larger, the CCC‐r chart becomes more sensitive to small changes of upward shift in p. However, since many observations are required to obtain a plotting point on the chart, the cost is fairly high. For this trade‐off problem it is necessary to determine the optimal number of non‐conforming items observed before a point is plotted, the sampling (inspection) interval, and the lower control limit for the chart. In this paper a simplified optimal design method is proposed. For illustrative purposes, some numerical results for the optimal design parameter values are provided. The expected profits per cycle obtained using the proposed optimal design method are compared with those obtained using other misspecified parameter values. The effects of changing these parameters on the profit function are shown graphically. Copyright © 2001 John Wiley & Sons, Ltd.     

The Design of the S2 Control Charts Based on Conditional Performance via Exact Methods

In this paper, we consider the conditional performance of the equal‐tailed and average run lengths (ARL)‐unbiased two‐sided S² charts when the in‐control variance of a normal process is estimated. We derive the exact probability distributions of the conditional ARL for the two S² charts. Then we evaluate the performance of each S² chart in terms of the percentiles, mean and standard deviation of the conditional in‐control ARL distribution. Because the parameter estimation seriously affects the conditional performance of these S² charts, we propose an exact method to design the equal‐tailed and ARL‐unbiased S² charts with desired conditional in‐control performance. The results indicate that the new ARL‐unbiased S² chart has far smaller standard deviation ARL values and the unconditional ARL values are more close to the desired value than the corresponding new equal‐tailed S² chart. Copyright © 2017 John Wiley & Sons, Ltd.     

CUSUM charts for monitoring a zero‐inflated poisson process

A zero‐inflated Poisson (ZIP) process is different from a standard Poisson process in that it results in a greater number of zeros. It can be used to model defect counts in manufacturing processes with occasional occurrences of non‐conforming products. ZIP models have been developed assuming that random shocks occur independently with probability p, and the number of non‐conformities in a product subject to a random shock follows a Poisson distribution with parameter λ. In our paper, a control charting procedure using a combination of two cumulative sum (CUSUM) charts is proposed for monitoring increases in the two parameters of the ZIP process. Furthermore, we consider a single CUSUM chart for detecting simultaneous increases in the two parameters. Simulation results show that a ZIP‐Shewhart chart is insensitive to shifts in p and smaller shifts in λ in terms of the average number of observations to signal. Comparisons between the combined CUSUM method and the single CUSUM chart show that the latter's performance is worse when there are only increases in p, but better when there are only increases in λ or when both parameters increase. The combined CUSUM method, however, is much better than the single CUSUM chart when one parameter increases while the other decreases. Finally, we present a case study from the light‐emitting diode packaging industry. Copyright © 2011 John Wiley & Sons, Ltd.     

A GLR control chart for monitoring a multinomial process

The problem of detecting changes in the parameter p in a Bernoulli process with two possible categories for each observation has been extensively investigated in the SPC literature, but there is much less work on detecting changes in the vector parameter p in a multinomial process where there are more than two categories. A few papers have considered the case in which the direction of the change in p is known, but there is almost no work for the important case in which the direction of the change is unknown and individual observations are obtained. This paper proposes a multinomial generalized likelihood ratio (MGLR) control chart based on a likelihood ratio statistic for monitoring p when individual observations are obtained and the direction and size of the change in p are unknown. A set of 2‐sided Bernoulli cumulative sum (CUSUM) charts is proposed as a reasonable competitor of the MGLR chart. It is shown that the MGLR chart has better overall performance than the set of 2‐sided Bernoulli CUSUM charts over a wide range of unknown shifts. Equations are presented for obtaining the control limit of the MGLR chart when there are three or four components in p .     

CS‐EWMA Chart for Monitoring Process Dispersion

Control charts are the most extensively used technique to detect the presence of special cause variations in processes. They can be classified into memory and memoryless control charts. Cumulative sum and exponentially weighted moving average control charts are memory‐type control charts as their control structures are developed in such a way that the past information is not ignored as it is done in the case of memoryless control charts, like the Shewhart‐type control charts. The present study is based on the proposal of a new memory‐type control chart for process dispersion. This chart is named as CS‐EWMA chart as its plotting statistic is based on a cumulative sum of the exponentially weighted moving averages. Comparisons with other memory charts used to monitor the process dispersion are done by means of the average run length. An illustration of the proposed technique is done by applying the CS‐EWMA chart on a simulated dataset. Copyright © 2012 John Wiley & Sons, Ltd.     

Nonparametric Progressive Mean Control Chart for Monitoring Process Target

Nonparametric control charts are widely used when the parametric distribution of the quality characteristic of interest is questionable. In this study, we proposed a nonparametric progressive mean control chart, namely the nonparametric progressive mean chart, for efficient detection of disturbances in process location or target. The proposed chart is compared with the recently proposed nonparametric exponentially weighted moving average and nonparametric cumulative sum charts using different run length characteristics such as the average run length, standard deviation of the run length, and the percentile points of the run length distribution. The comparisons revealed that the proposed chart outperformed recent nonparametric exponentially weighted moving average and nonparametric cumulative sum charts, in terms of detecting the shifts in process target. A real life example concerning the fill heights of soft drink beverage bottles is also provided to illustrate the application of the proposed nonparametric control chart. Copyright © 2012 John Wiley & Sons, Ltd.     

A Generalized Likelihood Ratio Chart for Monitoring Bernoulli Processes

This paper considers the problem of monitoring the proportion p of nonconforming items when a continuous stream of Bernoulli observations is available and the objective is to effectively detect a wide range of increases in p. The proposed control chart is based on a generalized likelihood ratio (GLR) statistic obtained from a moving window of past Bernoulli observations. The Phase II performance of this chart in detecting sustained increases in p is evaluated using the steady state average number of observations to signal. Comparisons of the Bernoulli GLR chart to the Shewhart CCC‐r chart, the Bernoulli cumulative sum chart, and the Bernoulli exponentially weighted moving average chart show that the overall performance of the Bernoulli GLR chart is better than its competitors. In addition, methods are provided for designing the Bernoulli GLR chart so that this chart can be easily applied in practice. Copyright © 2012 John Wiley & Sons, Ltd.     

CUSUM control charts with variable sampling interval for monitoring the ratio of two normal variables

In many industrial manufacturing processes, the ratio between two normal random variables plays a key role in ensuring quality of products. Thus,  monitoring this ratio is an important task that is well worth considering. In this paper, we combine a variable sampling interval (VSI) strategy with a cumulative sum (CUSUM) scheme to create a new type of control chart for purpose of tracking the ratio between two normal variables. The average time to signal (ATS) and the expected average time to signal (EATS) criteria are used to evaluate the performance of the new VSI CUSUM RZ control chart. The  numerical results show that the proposed control chart has much more attractive performance in comparison with the standard CUSUM-RZ control chart and the VSI EWMA-RZ control chart.